When the supply frequency increases, what happens to the capacitive reactance in the circuit?

Question

Examoogle · Accepted Answer

Decreases

Explanation: Capacitive reactance ($X_C$) is defined as the opposition offered by a capacitor to the flow of alternating current. It is inversely proportional to the frequency ($f$) of the supply voltage.

Working Principle: The capacitive reactance is given by the formula $X_C = \frac{1}{2\pi fC}$. As the frequency ($f$) increases, the denominator of this expression increases, which causes the value of $X_C$ to decrease. Physically, at higher frequencies, the charge on the capacitor plates changes more rapidly, resulting in higher current flow for a given voltage, signifying lower opposition.

Key Formulas: $X_C = \frac{1}{2\pi fC}$ — The capacitive reactance formula where $f$ is frequency in Hz and $C$ is capacitance in Farads.

Key Points: Capacitive reactance is inversely proportional to frequency.; For DC circuits ($f=0$), $X_C$ becomes infinite, acting as an open circuit.; Higher frequency allows more current to pass through the capacitor.; The unit of capacitive reactance is Ohms ($\Omega$).

Advantages: Useful in high-pass filter designs.; Effective for blocking DC in coupling applications.

Disadvantages: Excessive capacitive current at high frequencies can cause heating in power systems.; Sensitive to frequency variations in tuned circuits.

Applications: Coupling capacitors in amplifiers.; Frequency-selective filters.; Power factor correction in electrical networks.

Additional Info: The frequency sensitivity of capacitors is the fundamental principle behind capacitive reactance-based voltage dividers.. Option A is incorrect because it describes inductive reactance ($X_L = 2\pi fL$). Option C implies frequency independence, which is false for reactive components.

Answer: B is correct — Capacitive reactance is inversely proportional to the supply frequency, so an increase in frequency leads to a decrease in reactance.

Exam Tip: Remember: Inductive reactance ($X_L$) increases with frequency, while Capacitive reactance ($X_C$) decreases with frequency. Use 'ELI the ICE man' to recall that current leads voltage in capacitive circuits.

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